Question

Two thin parallel slits that are 0.0117 mm apart are illuminated by a laser beam of wavelength 620 nm.

(a) On a very large distant screen, what is the total number of bright fringes (those indicating complete constructive interference), including the central fringe and those on both sides of it? Solve this problem without calculating all the angles! (Hint: What is the largest that sin ? can be? What does this tell you is the largest value of m?)
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(b) At what angle, relative to the original direction of the beam, will the fringe that is most distant from the central bright fringe occur?
± ____ °

Answer 1

The condition for diffraction is, dsin = m               ...(1)
For the largest value of m, sin = 1
ie, d = m
m = d/
= (117 x 10^-7) / (6.2 x 10^-7)
= 18.87 = 18
Total number of bright fringe on either side = 2 x 18 = 36
Total number including the central maxima = 36 + 1 = 37

b)
Substituting m = 18 in equation (1),
(117 x 10^-7) x sin = 18 x (6.2 x 10^-7)
sin = 111.6 / 117 = 0.954
= sin^-1(0.954)
= 72.52 degrees